Other mistake: There are two mistakes when Bart calls the Krusty Hotline: 1, The cereal box says the phone number is '1-909-O-U-KLOWN.' Bart presses eight buttons on the phone. 2, as he is dialing, you can HEAR seven buttons being pressed. (00:01:45)
Continuity mistake: When Mr. Burns notices that Homer is wearing a pink shirt to work, when he pauses and zooms in the video, Homer is looking almost directly at the camera. In the next shot, though, he is looking more to his left. The people surrounding him also change. (00:03:05)
Continuity mistake: Bart opens the house's front door, then the shot zooms out to show us that all of Springfield is at the Simpson house. In the next shot with Mayor Quimby the door is suddenly closed. (00:15:30)
Audio problem: When Bart says "Krusty Hotline" his mouth doesn't move.
Audio problem: When Homer is in the asylum talking in his sleep, his mouth stays open when he's talking.
Audio problem: When Michael and Bart are playing a song to Lisa, Bart uses her bin as a drum. Sometimes you hear tapping, but Bart doesn't touch the bin.
Continuity mistake: After "Michael" comes out of the Simpsons' car, there's a shot of the crowd's shocked reaction. Oddly, Groundskeeper Willie seems to have grey hair and brown skin.
Mr. Lisa Goes to Washington - S3-E2
Other mistake: The first time we see all three children staring at the TV, the interior of the Simpson house seems different. (00:02:30)
Mr. Lisa Goes to Washington - S3-E2
Audio problem: When Lisa is reading her speech for the essay contest, what she says does not match her mouth movements. (00:06:30)
Mr. Lisa Goes to Washington - S3-E2
Audio problem: When the lady is asking questions to Homer before Lisa wins the trip to Washington, what she says doesn't match her mouth. (00:07:20)
Mr. Lisa Goes to Washington - S3-E2
Continuity mistake: When Lisa approaches the Abe Lincoln statue, there is an old person near her. In the next shot, there are three people suddenly surrounding her. (00:15:05)
Mr. Lisa Goes to Washington - S3-E2
Plot hole: The Simpsons take a flight to Washington D.C. for Lisa's speech. But it is revealed in a later episode that Marge has a Fear of Flying. This was before it was discovered that she had a Fear of Flying.
Mr. Lisa Goes to Washington - S3-E2
Factual error: When the piano keys are shown when it is played at the end of the episode, it is shown having one black key each time. Real pianos start off with three black keys, then two, then three and so on.
Continuity mistake: At the beginning, when there is an overhead shot of the Simpsons' lawn, the broken lawn mower has disappeared. (00:01:20)
Audio problem: During Marge and Homer's argument at the beginning, when Homer says that Ned Flanders is a jerk, his mouth doesn't match what he's saying. (00:01:55)
Continuity mistake: When Homer is on the sofa, the cushion under his head disappears when he wakes up. (00:03:00)
Continuity mistake: When Bart taunts Homer, he has nothing on his plate apart from his burger. When Homer runs over a second later there is more stuff on his plate. (00:03:30)
Continuity mistake: When Homer is smelling the BBQ the smoke that's in front of him vanishes instantly. (00:03:30)
Continuity mistake: When Homer is hanging out of the window there is a blue curtain tie visible however this disappears in the long shot. (00:03:30)
Continuity mistake: When Ned starts talking about the Leftorium during his barbecue, Marge's dress is pink in one shot. (00:04:05)
Answer: I'm not sure if this is the one you're thinking of, but an episode of "Ray Bradbury Theatre," called "A Sound of Thunder," dealt with a similar matter: a group of hunters travel back in time to hunt dinosaurs, only to find things have changed when they get back because someone stepped on a butterfly.
Xofer